## Functiones et Approximatio Commentarii Mathematici

### Bounding the least prime ideal in the Chebotarev Density Theorem

Asif Zaman

#### Abstract

Let $K$ be a number field and suppose $L/K$ is a finite Galois extension. We establish a bound for the least prime ideal occurring in the Chebotarev Density Theorem. Namely, for every conjugacy class $C$ of $\mathrm{Gal}(L/K)$, there exists a prime ideal $\mathfrak{p}$ of $K$ unramified in $L$, for which its Artin symbol $\big[ \frac{L/K}{\mathfrak{p}} \big] = C$, for which its norm $N^K_{\mathbb{Q}}\mathfrak{p}$ is a rational prime, and which satisfies $N^K_{\mathbb{Q}} \mathfrak{p} \ll d_L^{40},$ where $d_L = |\mathrm{disc}(L/\mathbb{Q})|$. All implicit constants are effective and absolute.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 57, Number 1 (2017), 115-142.

Dates
First available in Project Euclid: 28 March 2017

https://projecteuclid.org/euclid.facm/1490688030

Digital Object Identifier
doi:10.7169/facm/1651

Mathematical Reviews number (MathSciNet)
MR3704230

Zentralblatt MATH identifier
06864168

#### Citation

Zaman, Asif. Bounding the least prime ideal in the Chebotarev Density Theorem. Funct. Approx. Comment. Math. 57 (2017), no. 1, 115--142. doi:10.7169/facm/1651. https://projecteuclid.org/euclid.facm/1490688030

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